Geometric methods in statistical learning theory and applications

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This project aims at developing differential geometric methods in statistical learning theory, in particular in the geometry of efficient estimators. When investigating large amounts of data, it is essential to find a density function representing the structure of the data. This is done by giving a so called estimator, based on some feature function of the data. The efficiency of this estimator is then defined in terms of the deviation of the estimated from the actual density.In recent years, differential geometric methods were developed for constructing efficient estimators, and it is the aim of the present project to refine these methods. In particular, we wish to investigate exponential models and the geometry of the natural gradient flow, and apply them to machine learning.